Non-null test of cylindrical surfaces with complex parameters based on pseudo shearing interferometry

Cylindrical surfaces with complex parameters (CSCP), including off-axis, aspheric, and other properties, provide higher degrees of design freedom than cylindrical surfaces with spherical cross-sections. Thus, they can better satisfy the requirements of complex optical systems. To the best of our knowledge, we present a novel non-null test method for the CSCP: two-dimensional pseudo lateral shearing interferometry (2DPLSI). During the measurement process, the test surface translates along orthogonal directions, and the figure error is reconstructed by a method similar to lateral shearing interferometry. Our approach strongly reduces the retrace error inherent to non-null test and other errors, including the figure error of the compensating lens and the system error. The reduction of errors facilitates the design of the compensating lens, and a spherical cylinder suffices to meet the requirements. Furthermore, we analyze the misalignment aberrations introduced by the orthogonal displacement in non-null interferometry and propose a calibration method to achieve high precision measurement. The experimental results demonstrate that the root-mean-square (RMS) value of the difference map compared with null test is better than λ/50 (λ = 632.8 nm), and the repeatability of the proposed method is superior to λ/200 RMS.